Effects Of Dipole-dipole Interaction On Steady State Populations Of Two-atom-cavity System

For the past few years, with great experimental progresses in laser cooling and trapping atoms, high precision manipulating atoms, engineering the strong interaction between photons and atoms and preparing quantum entanglement in many-body systems, the studying on photons interact with a large number of atoms confined in a region of ultra-small space arouses people’s great interests. The interaction between light and matter will lead to more rich and interesting physical phenomena due to the influence of the competing between the cooperative effects of atoms and the atom-photon interaction. And the dipole-coupled two-atom system can serve as a basic building block in understanding the effects among interacting atoms, so it is necessary to investigate the dipole-coupled atoms deeply.The eigenstates of the two two-level atoms system with dipole-dipole interaction can be usually called as Dicke states, or collective states. Within the Dicke state representation, the two two-level atoms can be modeled as an effective four-level atom system.In this paper, by employing the master equation approach we obtained the dynamic equation of the two identical atomic system driven by an external coherent laser field and the system of two identical two-level cooperative systems interacting via the dipole-dipole interaction coupling with a cavity field under the basis of Dicke states, respectively. Then a steady state analysis on the influence of dipole-dipole interaction for level population is investigated.We assume that the cavity is very weakly driven for the case of two-atom coupled with a cavity field. In this case, acting on the T-C Model, we take the expectation value of the level population dynamical equations for coupled systems interacting with the environment. We also made a comparative analysis on the steady states level populations corresponding to the classical driven field.